Echoing Red Dawn, one could say that China's massive population (which quite possibly could've grown prior to the 2077 Great War, unless the communist regime resorts to a "one child policy" prior to the timeline's global nuclear engagement) of roughly a billion souls could very much so be reduced in size by U.S. nukes to a mere six hundred million people.
The communist Chinese government could be said to have survived, fairly intact, the leadership residing in various safe havens scattered across the mainland not too dissimilar to the designated evacuation points in the U.S. during the Cold War such as Raven Rock and the Cheyenne Mountain nuclear bunker complex.
Major cities, especially those along the coast, would be engulfed in nuclear fire, irradiating the surrounding landscape for miles.
Beijing, evacuated by the government, would be ravaged (but still standing, as opposed to just being a giant crater, owing to the Fallout universe's weaker nuclear weapons)
Its implied in Fallout 3 that the National Guard attempted to assert some degree of order in the capital, trying in vain to clean up radiation while protecting survivors in D.C. and its surrounding environs.
Possibly local governmental structures could have survived, in constant contact with the central government, struggling to provide even the mere semblance of law and order. This as well is also hinted at in Fallout 3, where it is stated that the National Guard was still receiving orders from the government for awhile after the nuclear bombardment of D.C.
The People's Liberation Army could try something similar, buttressed by local law enforcement, however pointless.
That being said, in the immediate days, weeks, and months after the Great War those survivors lucky enough to have escaped the cities would have streamed into the countryside in search of food, shelter, and protection in a more or less lawless postwar world.
Many that didn't perish in the atomic fire storms or from severe radiation sickness would promptly die of mass starvation as the villages proved incapable of feeding this vast sea of humanity.
There might also have been something similar to the Vault Project in China, although one entirely reliant on the government rather than private interests, allowing for many people to live out the first several years underground in relative safety.
Does that mean that these vaults would also be prone to experimentation? Not necessarily, because as far as we know only the United States government was hellbent on conducting tests on vault denizens in the interest of leaving Earth behind. The Chinese government could have built them for the original purpose that they were intended for, to save as much of the populace as possible.
And, like in the U.S. with or without an Enclave conspiracy, a good number of vaults would nonetheless open on schedule once the fallout cleared, possibly containing something similar to the Garden of Eden Creation Kit (Considering what we know about China's infiltration tactics in D.C. and Hoover Dam, its not unlikely that the tech could be stolen and then reverse engineered)
Eventually things would begin to settle down as in the U.S. Survivalist communities would form, pockets of civilization in a shattered land.
The government might collapse, or it might not, but much of the surviving Chinese citizens would be on their own. The cities would be nothing more then abandoned ruins, the countryside wracked by squalor, lawlessness, and famine.
Who knows what China would look like by the time of New Vegas. A lot could have happened with that 200+ year time span. Maybe the government takes up leadership once again. Or perhaps a strong, centralized nation state is formed independently.
We don't know, as its mere speculation, until they make a game set in post apocalyptic China (which may never happen)
